Disabling Sharing Name for mobile admins.

I assume you meant 'changing' and not 'hanging' their sharing names.
If so, you could go the hammer approach and use a Config Profile to lock down the entire Sharing Preference Pane. There is unfortunately no way to only disable the field to change the Sharing name in the Pref Pane. Its an all or nothing proposition if you lock it down. So that may or may not work for you.

Another possibility would be to have a policy or even a local process that checks the sharing name against a known string, maybe something written into a local file that contains the name the Mac should have. If it sees its different, flip it back to the known name. It won't stop them from renaming it, but it would put it back to the way its supposed to be. Since you mentioned mobile admins, I assume you mean cached AD mobile accounts. That would mean the Macs are joined to AD, so there should already be a name you can use for this from dsconfigad for example.

There may be a few other approaches others will post. Ultimately, this comes down to a people issue and not a technical one. Do you have some policy guidelines in place, like an AUP for what end users can and cannot do to their systems? I've found that if you don't have something like that in place, its an open invitation for admin users to do what they want to their computers. Effectively, if its not against company rules, they assume they can do it.

Thanks. yes, I meant "changing" (edit made) :)

Disabling the entire Sharing Pref Pane is just fine. When we crate a Config Profile using the JSS, the profile does not make the change on the client Mac. Is there something we are missing or need to do on the client other than installing the config file?

Well, how is it being deployed to the Mac? When you make a config profile in the JSS the assumption is you are pushing it over MDM, which requires using Apple's APNs process, so there are some steps you need to take to get that all set up. Its not just set up out of the box. Even with all that in place, there is still scope to consider.

If you're looking to install it manually from a .mobileconfig file, that's also possible, but it would need to be pulled down from the JSS and put into some kind of package that would drop the mobileconfig file into a location like /tmp/ and then install it using the profiles command. That's just one way, but generally the most used way when talking about installing profiles outside of Apple's push process.